you can also check this site out
http://www.cheekiemonkie.net/. The site has a lot of pictures. It gives you a good idea of the places to see and things to do.
We went around a lot of parks (bishan park, hort park, jacob ballas garden etc) and indoors when raining (royce@liang court good for the younger ones, Amazonia @greatworld city with the big slide). The terminal 1 at changi airport also has a playarea that is free to use but gets a bit crowded.
Some of the malls also have small playareas paragon@orchard, nex@serangoon (water play).
We also had the zoo membership, the water playarea at the zoo is fun especially on a hot day.